A key perspective of deep learning is representation learning, where concepts or entities are embedded in latent space and are represented by latent vectors whose units can be interpreted as neurons. In this talk, I will discuss our recent work on representation learning for grid cells. The grid cells in the mammalian entorhinal cortex exhibit striking hexagon firing patterns when the agent (e.g., a rat or a human) navigates in the open field. I will explain that the grid cells form a position embedding or position2vec. The vector is driven by a recurrent network as the agent undergoes self-motion. We identity an isotropy condition for the recurrent network that leads to locally conformal embedding and that underlies the hexagon grid patterns. Joint work with Ruiqi Gao, Jianwen Xie, Xue-Xin Wei and Song-Chun Zhu.

Ying Nian Wu is currently a professor in Department of Statistics, UCLA. He received his A.M. degree and Ph.D. degree in statistics from Harvard University in 1994 and 1996 respectively. He was an assistant professor in Department of Statistics, University of Michigan from 1997 to 1999. He joined UCLA in 1999. He has been a full professor since 2006. Wu’s research areas include generative modeling, representation learning, unsupervised learning, computer vision, computational neuroscience, and bioinformatics.